orbitdetermination

Orbit determination is the process of estimating the state vector of a spacecraft or body in space from measurements and a physical model of motion. In spacecraft operations, it encompasses initial orbit determination, successive orbit determination, and debris tracking. The goal is to produce a trajectory that can be propagated forward with quantified uncertainty.

Measurements used include radar and optical observations, such as range, Doppler, azimuth and elevation, or angular measurements. Spacecraft transponders provide tracking data; astrometric observations contribute to the estimate for objects in Earth orbit. Observables are linked to the state by a dynamical model and a measurement model, and the estimation procedure seeks to minimize residuals between observed and predicted measurements.

The dynamical model commonly starts from Newtonian gravity and may include perturbations: Earth's oblateness (J2), third-body gravitation from the Moon and Sun, solar radiation pressure, atmospheric drag for low earth orbiters, tides, and relativistic effects if needed. The state is usually expressed as a position and velocity (ECI) or as orbital elements.

Estimation methods include analytical initial orbit determination techniques such as the Gauss or Laplace methods, and numerical approaches based on batch least squares or differential corrections. Sequential methods such as Kalman filtering and its variants are used for continuous updating with new data.

Outputs include state vectors, orbital elements, and their covariance, with accuracy depending on measurement quality, model fidelity, and data arc length. OD supports mission planning, maneuver budgeting, conjunction assessment, and trajectory prediction. Software tools such as SPICE, GMAT, and STK are commonly used in the field.